{"title":"Elementary divisors, Hochster duality, and spectra","authors":"Wolfgang Rump","doi":"10.1007/s00013-024-02052-3","DOIUrl":null,"url":null,"abstract":"<div><p>It is proved that every Bézout domain admits an embedding into an elementary divisor domain with the same divisibility group. So the prime spectrum of a Bézout domain is homeomorphic to the prime spectrum of an elementary divisor domain. Together with an earlier result, it follows that a topological space is homeomorphic to the maximal spectrum of an elementary divisor domain if and only if it is a serial quasi-compact <span>\\(T_1\\)</span>-space.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-02052-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
It is proved that every Bézout domain admits an embedding into an elementary divisor domain with the same divisibility group. So the prime spectrum of a Bézout domain is homeomorphic to the prime spectrum of an elementary divisor domain. Together with an earlier result, it follows that a topological space is homeomorphic to the maximal spectrum of an elementary divisor domain if and only if it is a serial quasi-compact \(T_1\)-space.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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